Cannot get rid of smoothing. But why? (not: "But how?")
"Sharp Edges" only works in correlation with the option "Auto Smooth" enabled. 
Auto Smooth uses the angle of edges standing on each other to determine if they should be shaded flat or smooth. The input "angle" is the starting point, so if the angle > 50° the faces will be shaded smooth

You could see the option "mark sharp" as an overwrite for the auto-smooth shading. "mark smooth" is essentially just a reset to default, or in this case the shading determined by the auto-smooth. Thats why only mark sharp has a visual edge highlight in the viewport.